Interaction Improves Two-party Nonparametric Pointwise Density Estimation

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We characterize the minimax rates in two-party nonparametric pointwise density estimation in terms of the communication costs, under either the one-way or interactive protocols. It is shown that allowing interactive communications can strictly improve the minimax rate, a phenomenon not seen the parametric counterpart of the problem (assuming that the parameters are fixed). Moreover, a few rounds of interactions achieve the interactive minimax rate: the number of rounds can grow as slowly as the super-logarithm (i.e., inverse tetration) of k. The proof of the upper bound is based on a novel multi-round scheme for estimating the joint distribution of a pair of biased Bernoulli variables.

Original languageEnglish (US)
Title of host publication2022 IEEE International Symposium on Information Theory, ISIT 2022
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages904-909
Number of pages6
ISBN (Electronic)9781665421591
DOIs
StatePublished - 2022
Event2022 IEEE International Symposium on Information Theory, ISIT 2022 - Espoo, Finland
Duration: Jun 26 2022Jul 1 2022

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
Volume2022-June
ISSN (Print)2157-8095

Conference

Conference2022 IEEE International Symposium on Information Theory, ISIT 2022
Country/TerritoryFinland
CityEspoo
Period6/26/227/1/22

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Information Systems
  • Modeling and Simulation
  • Applied Mathematics

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